Use this page to understand how DB Precision develops dependent decrement probabilities, active survival, and mid-year valuation quantities.
When more than one active decrement can occur during the same projection year, input decrement probabilities may be adjusted to reflect competition among the applicable decrements.
The Decrement Precedence selection determines which input rates participate in the competing-decrement adjustment.
Adjust all rates — Applies the competition formula to mortality, termination, disability, and retirement. A raw retirement rate of 100% sets the competing mortality, termination, and disability probabilities to zero for that year.
Do not adjust any rates — Uses each annual input rate directly as its decrement probability.
Only adjust mortality — Applies the competition formula to active mortality and uses the other three rates without adjustment.
- q′(d)x
- is the single-decrement probability for decrement d at age x, before allowance for competing decrements.
- q(d)x
- is the resulting probability of decrement d at age x, after allowance for competing decrements.
- q′(j)x
- is the single-decrement probability for competing decrement j at age x. These probabilities are summed across all applicable competing decrements other than decrement d.
- k
- is the decrement timing factor: one-half for Mid-Year Decrement Timing and 1 for beginning-of-year decrement timing.
The calculation is applied separately to each decrement subject to competition under the selected Decrement Precedence setting.
After the applicable dependent decrement probabilities have been developed, active survival is determined from the decrements that apply during each projection year.
- tp(τ)x
- is the probability that a participant aged x remains active for t years under all applicable active decrements.
- q(d)x+t
- is the dependent probability for active decrement d at age x+t. These probabilities are summed across all active decrements applicable during that year.
Only decrements applicable during a projection year reduce active survival. For example, retirement is included only when an applicable retirement benefit is available.
The cumulative active-survival and dependent-decrement terms developed here are used in the PVFB, UC, PUC, and VBO formulas.
When Mid-Year Decrement Timing is selected, DB Precision assumes active decrements occur, on average, halfway through the projection year. For applicable quantities evaluated at annual projection dates, DB Precision approximates the mid-year value by averaging the current-year and next-year values.
- Yt
- is an annually evaluated quantity at projection duration t.
Benefit amounts and adjustments — For benefit amounts, Yt represents the amount payable at the annual projection date. The mid-year benefit is used when the decrement is assumed to occur during the year, with analogous treatment for UC-attributed benefits. For benefit adjustments, Yt represents the applicable early or late retirement adjustment. Separate mid-year adjustment values are developed where needed for UC and VBO calculations.
Vesting — Vesting is handled differently. DB Precision evaluates the applicable vesting formula at the actual date six months after the beginning of the projection year rather than averaging beginning- and end-of-year vesting percentages.
Active exposure for EAN — DB Precision averages beginning- and end-of-year active survival when developing mid-year active exposure for PVFS or PV Service.
Mid-year timing is also reflected in discounting and the construction of applicable Benefit Payment Form values. DB Precision develops current- and next-year discount factors and applies half-year timing within the applicable payment-form calculation. The exact treatment depends on the decrement and form of payment.